It puts power to both wheels, instead of just the one that has less grip, like open differentials do. I got it becasue I race autocross, and it makes a big difference in tight corners. I don't know technically how it works, but it has more gears than an open diff. Mine is a helical design.

Most limited slip diffs use clutches to ensure that at least some torque always goes to the wheel with better traction. Clutches create friction and heat so that they probably make mileage worse. There are some limited slip diffs that use worm gears instread of the usual bevel gears. Worm gears can lock if the reduction ratio is above about 5:1. These "Torsen" diffs don't use clutches, and they're probably neutral with regard to mpg.

I have a factory limited slip diff on the F350, but it feels like its worn out. I had to rock back and forth to get out of a snowbank today, and one of the wheels was on asphalt! If I replace it, I'll probably switch to an air locker. This is an open diff that locks the axles together... "no slip" ... with an air cylinder.

That's what I was hoping for, since mine isn't the clutch type. I am just concerned that with the extra worm gers, there would be more friction. I don't think there would be that much extra friction, though. I'm trying to find a picture of it.

hmm prolly not that much different. i was thinking in turns liek a simple right turn on a street or sharp turn on roads that it would cause the car to slow down more when u turned due to the differential...im not sure what would happen im just speculating...

The helical gears (or clutches) revolve with the ring gear when there is no difference in axle speeds from turning. There will be no true friction drag when driving straight.
The amount of distance and the duration of time actually spent turning sharp corners is quite low so even a moderate amount of resistance in the clutches or the helices during these times will not have a large effect on overall mileage.

These are limited slip, not zero slip as a locker would be, so some turning difference in axle speeds is tolerated before the mechanisms fully engage.

The helical gears (or clutches) revolve with the ring gear when there is no difference in axle speeds from turning. There will be no true friction drag when driving straight.
The amount of distance and the duration of time actually spent turning sharp corners is quite low so even a moderate amount of resistance in the clutches or the helices during these times will not have a large effect on overall mileage.

These are limited slip, not zero slip as a locker would be, so some turning difference in axle speeds is tolerated before the mechanisms fully engage.

yea thats what i was thinking but i wasnt sure how a limited slip behaved

In summary, the bigger the speed difference between the two axles, the harder the clutches engage. You can change things (i.e. spring rates etc.) inside the differential to control how the clutches will engage, however even under a slight corner there isn't really any drag.

One other thing to watch out for - in many types of rearends, a LSD cannot use synthetic fluid because it is too slippery. Use the fluid recommended by your manufacturer.